An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted

Free surface flow past topography : a beyond-all-orders approach

The problem of steady subcritical free surface flow past a submerged inclined step is considered. The asymptotic limit of small Froude number is treated, with particular emphasis on the effect that changing the angle of the step face has on the surface waves. As demonstrated by Chapman & Vanden-Broeck (2006), the divergence of a power series expansion in powers of the square of the Froude number is caused by singularities in the analytic continuation of the free surface; for an inclined step, these singularities may correspond to either the corners or stagnation points of the step, or both, depending on the angle of incline. Stokes lines emanate from these singularities, and exponentially small waves are switched on at the point the Stokes lines intersect with the free surface. Our results suggest that for a certain range of step angles, two wavetrains are switched on, but the exponentially subdominant one is switched on first, leading to an intermediate wavetrain not previously noted. We extend these ideas to the problem of flow over a submerged bump or trench, again with inclined sides. This time there may be two, three or four active Stokes lines, depending on the inclination angles. We demonstrate how to construct a base topography such that wave contributions from separate Stokes lines are of equal magnitude but opposite phase, thus cancelling out. Our asymptotic results are complemented by numerical solutions to the fully nonlinear equations.

Analysis of large-amplitude stratospheric mountain wave event observed from the AIRS and MLS sounders over the western Himalayan region

Mountain waves in the stratosphere have been observed over elevated topographies using both nadir-looking and limb-viewing satellites. However, the characteristics of mountain waves generated over the Himalayan Mountain range and the adjacent Tibetan Plateau are relatively less explored. The present study reports on three-dimensional (3-D) properties of a mountain wave event that occurred over the western Himalayan region on 9 December 2008. Observations made by the Atmospheric Infrared Sounder on board the Aqua and Microwave Limb Sounder on board the Aura satellites are used to delineate the wave properties. The observed wave properties such as horizontal (lambda(x), lambda(y)) and vertical (lambda(z)) wavelengths are 276 km (zonal), 289 km (meridional), and 25 km, respectively. A good agreement is found between the observed and modeled/analyzed vertical wavelength for a stationary gravity wave determined using the Modern Era Retrospective Analysis for Research and Applications (MERRA) reanalysis winds. The analysis of both the National Centers for Environmental Prediction/National Center for Atmospheric Research reanalysis and MERRA winds shows that the waves are primarily forced by strong flow across the topography. Using the 3-D properties of waves and the corrected temperature amplitudes, we estimated wave momentum fluxes of the order of similar to 0.05 Pa, which is in agreement with large-amplitude mountain wave events reported elsewhere. In this regard, the present study is considered to be very much informative to the gravity wave drag schemes employed in current general circulation models for this region.

Analysis of large-amplitude stratospheric mountain wave event observed from the AIRS and MLS sounders over the western Himalayan region

Mountain waves in the stratosphere have been observed over elevated topographies using both nadir-looking and limb-viewing satellites. However, the characteristics of mountain waves generated over the Himalayan Mountain range and the adjacent Tibetan Plateau are relatively less explored. The present study reports on three-dimensional (3-D) properties of a mountain wave event that occurred over the western Himalayan region on 9 December 2008. Observations made by the Atmospheric Infrared Sounder on board the Aqua and Microwave Limb Sounder on board the Aura satellites are used to delineate the wave properties. The observed wave properties such as horizontal (lambda(x), lambda(y)) and vertical (lambda(z)) wavelengths are 276 km (zonal), 289 km (meridional), and 25 km, respectively. A good agreement is found between the observed and modeled/analyzed vertical wavelength for a stationary gravity wave determined using the Modern Era Retrospective Analysis for Research and Applications (MERRA) reanalysis winds. The analysis of both the National Centers for Environmental Prediction/National Center for Atmospheric Research reanalysis and MERRA winds shows that the waves are primarily forced by strong flow across the topography. Using the 3-D properties of waves and the corrected temperature amplitudes, we estimated wave momentum fluxes of the order of similar to 0.05 Pa, which is in agreement with large-amplitude mountain wave events reported elsewhere. In this regard, the present study is considered to be very much informative to the gravity wave drag schemes employed in current general circulation models for this region.

The role of Qiongzhou Strait in the seasonal variation of the South China Sea circulation

An analysis of the water level and current data taken in Qiongzhou Strait in the South China Sea (SCS) over the last 37 years (1963 to 1999) was made to examine the characteristics of tidal waves and residual flow through the strait and their roles in the seasonal variation of the SCS circulation. The observations reveal that Qiongzhou Strait is an area where opposing tidal waves interact and a source of water transport to the Gulf of Beibu (Gulf of Tonkin), SCS. A year-round westward mean flow with a maximum speed of 10-40 cm s(-1) is found in Qiongzhou Strait. This accounts for water transport of 0.2-0.4 Sv and 0.1-0.2 Sv into the Gulf of Beibu in winter-spring and summer-autumn, respectively. The outflow from Qiongzhou Strait may cause up to 44% of the gulf water to be refreshed each season, suggesting that it has a significant impact on the seasonal circulation in the Gulf of Beibu. This finding is in contrast to our current understanding that the seasonal circulation patterns in the South China Sea are primarily driven by seasonal winds. Several numerical experiments were conducted to examine the physical mechanisms responsible for the formation of the westward mean flow in Qiongzhou Strait. The model provides a reasonable simulation of semidiurnal and diurnal tidal waves in the strait and the predicted residual flow generally agrees with the observed mean flow. An analysis of the momentum equations indicates that the strong westward flow is driven mainly by tidal rectification over variable bottom topography. Both observations and modeling suggest that the coastal physical processes associated with tidal rectification and buoyancy input must be taken into account when the mass balance of the SCS circulation is investigated, especially for the regional circulation in the Gulf of Beibu.

Validation of a regional Indonesian seas model based on a comparison between model and INSTANT transports

The International Nusantara Stratification and Transport (INSTANT) program measured currents through multiple Indonesian Seas passages simultaneously over a three-year period (from January 2004 to December 2006). The Indonesian Seas region has presented numerous challenges for numerical modelers - the Indonesian Throughflow (ITF) must pass over shallow sills, into deep basins, and through narrow constrictions on its way from the Pacific to the Indian Ocean. As an important region in the global climate puzzle, a number of models have been used to try and best simulate this throughflow. In an attempt to validate our model, we present a comparison between the transports calculated from our model and those calculated from the INSTANT in situ measurements at five passages within the Indonesian Seas (Labani Channel, Lifamatola Passage, Lombok Strait, Ornbai Strait, and Timor Passage). Our Princeton Ocean Model (POM) based regional Indonesian Seas model was originally developed to analyze the influence of bottom topography on the temperature and salinity distributions in the Indonesian seas region, to disclose the path of the South Pacific Water from the continuation of the New Guinea Coastal Current entering the region of interest up to the Lifamatola Passage, and to assess the role of the pressure head in driving the ITF and in determining its total transport. Previous studies found that this model reasonably represents the general long-term flow (seasons) through this region. The INSTANT transports were compared to the results of this regional model over multiple timescales. Overall trends are somewhat represented but changes on timescales shorter than seasonal (three months) and longer than annual were not considered in our model. Normal velocities through each passage during every season are plotted. Daily volume transports and transport-weighted temperature and salinity are plotted and seasonal averages are tabulated.

The spacing of orographic rainbands triggered by small-scale topography

A combination of idealized numerical simulations and analytical theory is used to investigate the spacing between convective orographic rainbands over the Coastal Range of western Oregon. The simulations, which are idealized from an observed banded precipitation event over the Coastal Range, indicate that the atmospheric response to conditionally unstable flow over the mountain ridge depends strongly on the subridge-scale topographic forcing on the windward side of the ridge. When this small-scale terrain contains only a single scale (l) of terrain variability, the band spacing is identical to l, but when a spectrum of terrain scales are simultaneously present, the band spacing ranges between 5 and 10 km, a value that is consistent with observations. Based on the simulations, an inviscid linear model is developed to provide a physical basis for understanding the scale selection of the rainbands. This analytical model, which captures the transition from lee waves upstream of the orographic cloud to moist convection within it, reveals that the spacing of orographic rainbands depends on both the projection of lee-wave energy onto the unstable cap cloud and the growth rate of unstable perturbations within the cloud. The linear model is used in tandem with numerical simulations to determine the sensitivity of the band spacing to a number of environmental and terrain-related parameters.

Mean flow and turbulence statistics over groups of urban-like cubical obstacles

Direct numerical simulations of turbulent flow over regular arrays of urban-like, cubical obstacles are reported. Results are analysed in terms of a formal spatial averaging procedure to enable interpretation of the flow within the arrays as a canopy flow, and of the flow above as a rough wall boundary layer. Spatial averages of the mean velocity, turbulent stresses and pressure drag are computed. The statistics compare very well with data from wind-tunnel experiments. Within the arrays the time-averaged flow structure gives rise to significant 'dispersive stress' whereas above the Reynolds stress dominates. The mean flow structure and turbulence statistics depend significantly on the layout of the cubes. Unsteady effects are important, especially in the lower canopy layer where turbulent fluctuations dominate over the mean flow.

The gravity wave momentum flux in hydrostatic flow with directional shear over elliptical mountains

Semi-analytical expressions for the momentum flux associated with orographic internal gravity waves, and closed analytical expressions for its divergence, are derived for inviscid, stationary, hydrostatic, directionally-sheared flow over mountains with an elliptical horizontal cross-section. These calculations, obtained using linear theory conjugated with a third-order WKB approximation, are valid for relatively slowly-varying, but otherwise generic wind profiles, and given in a form that is straightforward to implement in drag parametrization schemes. When normalized by the surface drag in the absence of shear, a quantity that is calculated routinely in existing drag parametrizations, the momentum flux becomes independent of the detailed shape of the orography. Unlike linear theory in the Ri → ∞ limit, the present calculations account for shear-induced amplification or reduction of the surface drag, and partial absorption of the wave momentum flux at critical levels. Profiles of the normalized momentum fluxes obtained using this model and a linear numerical model without the WKB approximation are evaluated and compared for two idealized wind profiles with directional shear, for different Richardson numbers (Ri). Agreement is found to be excellent for the first wind profile (where one of the wind components varies linearly) down to Ri = 0.5, while not so satisfactory, but still showing a large improvement relative to the Ri → ∞ limit, for the second wind profile (where the wind turns with height at a constant rate keeping a constant magnitude). These results are complementary, in the Ri > O(1) parameter range, to Broad’s generalization of the Eliassen–Palm theorem to 3D flow. They should contribute to improve drag parametrizations used in global weather and climate prediction models.

Mean sortable silt values from Holocene and glacial Scotia Sea sediments

The Antarctic Circumpolar Current is key to the mixing and ventilation of the world's oceans. This current flows from west to east between about 45° and 70° S connecting the Atlantic, Pacific and Indian oceans, and is driven by westerly winds and buoyancy forcing. High levels of productivity in the current regulate atmospheric CO2 concentrations. Reconstructions of the current during the last glacial period suggest that flow speeds were faster or similar to present, and it is uncertain whether the strength and position of the westerly winds changed. Here we reconstruct Antarctic Circumpolar Current bottom speeds through the constricting Drake Passage and Scotia Sea during the Last Glacial Maximum and Holocene based on the mean grain size of sortable silt from a suite of sediment cores. We find essentially no change in bottom flow speeds through the region, and, given that the momentum imparted by winds, and modulated by sea-ice cover, is balanced by the interaction of these flows with the seabed, this argues against substantial changes in wind stress. However, glacial flow speeds in the sea-ice zone south of 56° S were significantly slower than present, whereas flow in the north was faster, but not significantly so. We suggest that slower flow over the rough topography south of 56° S may have reduced diapycnal mixing in this region during the last glacial period, possibly reducing the diapycnal contribution to the Southern Ocean overturning circulation.

Sea-surface temperature reconstruction in the Southwest Pacific

Uniquely in the Southern Hemisphere the New Zealand micro-continent spans the interface between a subtropical gyre and the Subantarctic Circumpolar Current. Its 20° latitudinal extent includes a complex of submerged plateaux, ridges, saddles and basins which, in the present interglacial, are partial barriers to circulation and steer the Subtropical (STF) and Subantarctic (SAF) fronts. This configuration offers a singular opportunity to assess the influence of bottom topography on oceanic circulation through Pleistocene glacial - interglacial (G/I) cycles, its effect on the location and strength of the fronts, and its ability to generate significant differences in mixed layer thermal history over short distances. For this study we use new planktic foraminiferal based sea-surface temperature (SST) estimates spanning the past 1 million years from a latitudinal transect of four deep ocean drilling sites. We conclude that: 1. the effect of the New Zealand landmass was to deflect the water masses south around the bathymetric impediments; 2. the effect of a shallow submerged ridge on the down-current side (Chatham Rise), was to dynamically trap the STF along its crest, in stark contrast to the usual glacial-interglacial (G-I) meridional migration that occurs in the open ocean; 3. the effect of more deeply submerged, downstream plateaux (Campbell, Bounty) was to dynamically trap the SAF along its steep southeastern margin; 4. the effects of saddles across the submarine plateaux was to facilitate the development of jets of subtropical and subantarctic surface water through the fronts, forming localized downstream gyres or eddies during different phases in the G-I climate cycles; 5. the deep Pukaki Saddle across the Campbell-Bounty Plateaux guided a branch of the SAF to flow northwards during each glacial, to form a strong gyre of circumpolar surface water in the Bounty Trough, especially during the mid-Pleistocene Climate Transition (MIS 22-16) when exceptionally high SST gradients existed across the STF; 6. the shallower Mernoo Saddle, at the western end of the Chatham Rise, provided a conduit for subtropical water to jet southwards across the STF in the warmest interglacial peaks (MIS 11, 5.5) and for subantarctic water to flow northwards during glacials; 7. although subtropical or subantarctic drivers can prevail at a particular phase of a G-I cycles, it appears that the Antarctic Circumpolar Current is the main influence on the regional hydrography. Thus complex submarine topography can affect distinct differences in the climate records over short distances with implications for using such records in interpreting global or regional trends. Conversely, the local topography can amplify the paleoclimate record in different ways in different places, thus enhancing its value for the study of more minor paleoceanographic influences that elsewhere are more difficult to detect. Such sites include DSDP 594, which like some other Southern Ocean sites, has the typical late Pleistocene asymmetrical saw-tooth G-I climate pattern transformed to a gap-tooth pattern of quasi-symmetrical interglacial spikes that interrupt extended periods of minimum glacial temperatures.

Atmospheric boundary layer development over a narrow coastal plain during onshore flow

A study of the structure of the daytime atmospheric boundary layer during onshore flow over a narrow coastal plain is presented. The main emphasis of the study is on the nature and causes of heating and cooling observed in the boundary layer temperature profiles. Measurements included vertical temperature profiles above at least two sites derived from radiosondes and aircraft, as well as surface estimates of radiative and sensible heat fluxes. Surface meteorological and pilot balloon data were also available, providing further evidence of short-term changes in atmospheric boundary layer structure. The Manawatu case was representative of autumnal anticyclonic conditions with weak pressure gradients, and illustrated typical diurnal development of a convective boundary layer over a coastal plain bordered by mountain ranges, with a transition from a stable nocturnal situation to a well-mixed profile in the afternoon. The profiles show surface input of heat propagating upwards through the boundary layer during the day, as well as entrainment of heat at the top associated with shear induced turbulence and/or penetrative convection. Applying a one-dimensional model, estimates of boundary layer heat budget components were obtained for four time periods during the day. Later periods were affected by cumulus cloud development at the top of the boundary layer, resulting in significant changes in individual components. Input of sensible heat from the surface decreased, while the addition of heat to the boundary layer from both cloud condensation and advection increased.